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Chapter 27 | Wave Optics angle of 18.4Âº to the direction of polarization. Verify this statement. beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain. 89. Show that if you have three polarizing filters, with the second at an angle of 45Âº to the first and the third at an angle of 90.0Âº to the first, the intensity of light passed by the first will be reduced to 25.0% of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.) I is the intensity of light transmitted by two polarizing filters with axes at an angle Î¸ and Iâ² is the intensity when the axes are at an angle 90.0ÂºâÎ¸, then I + Iâ² = I 0, the original intensity. (Hint: Use the 90. Prove that, if trigonometric identities cos (90.0ÂºâÎ¸) = sin Î¸ and cos Î¸ + sin Î¸ = 1. ) 2 2 91. At what angle will light reflected from diamond be completely polarized? 92. What is Brewsterâs angle for light traveling in water that is reflected from crown glass? 93. A scuba diver sees light reflected from the waterâs surface. At what angle will this light be completely polarized? 94. At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank? 95. Light reflected at 55.6Âº from a window is completely polarized. What is the windowâs index of refraction and the likely substance of which it is made? 96. (a) Light reflected at 62.5Âº from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water? 97. If Î¸ b is Brewsterâs angle for light reflected from the top of an interface between two substances, and Î¸â² b is Brewsterâs angle for light reflected from below, prove that Î¸ b + Î¸â² b = 90.0Âº. 98. Integrated Concepts If a polarizing filter reduces the intensity of polarized light to 50.0% of its original value, by how much are the electric and magnetic fields reduced? 99. Integrated Concepts Suppose you put on two pairs of Polaroid sunglasses with their axes at an angle of 15.0Âº . How much longer will it take the light to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics. 100. Integrated Concepts (a) On a day when the intensity of sunlight is 1.00 kW / m 2 , a circular lens 0.200 m in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of 20.0Âº. Assuming the sunlight is unpolarized and the polarizers are 100% efficient, what is the initial rate of heating of the water in ÂºC / s , assuming it is 80.0% absorbed? The aluminum 185